Method and system for optimizing dental aligner geometry

ABSTRACT

Method and system for establishing an initial position of a tooth, determining a target position of the tooth in a treatment plan, calculating a movement vector associated with the tooth movement from the initial position to the target position, determining a plurality of components corresponding to the movement vector, and determining a corresponding one or more positions of a respective one or more attachment devices relative to a surface plane of the tooth such that the one or more attachment devices engages with a dental appliance are provided.

PRIORITY

This application claims the benefit of U.S. Provisional PatentApplication No. 61/024,526, filed Jan. 29, 2008, and U.S. ProvisionalPatent Application No. 61/024,534, filed Jan. 29, 2008, the disclosuresof which are incorporated herein in their entirety for all purposes.

FIELD OF THE INVENTION

The present invention relates to computational orthodontics anddentistry.

BACKGROUND

In orthodontic treatment, a patient's teeth are moved from an initial toa final position using any of a variety of appliances. An applianceexerts force on the teeth by which one or more of them are moved or heldin place, as appropriate to the stage of treatment.

The mechanism of the orthodontic movement, as a result of one to onecorrelation between the tooth position and the appliance generation isthat the teeth are “squeezed” into the new configuration and held inplace, allowing the teeth sufficient time to adapt to the new position,before the process is repeated again as the teeth move progressivelyalong the various treatment stages of a treatment plan.

In the one to one correlation between the current treatment state andthe subsequent target or n+1 treatment stage, the adaptation of thedental appliance may include interactions between the plastic and thetooth geometry which is suboptimal for achieving n+1 tooth position, andis typically not factored into the correlation. This may be the case inparticular for larger distances of tooth movement, where the amount ofappliance distortion may lead to stretch and stress in the appliancewhereby some areas of the aligner are not in close contact with theteeth in critical and/or desirable areas. As a result, the teeth may notbe moveable to the desired target position. Moreover, the oppositeeffect may also exist, where the teeth may be in contact in areas whichare counterproductive to reaching the desired or target position.

In addition, the dental attachments are used primarily for changing thegeometry of the tooth crown to assure better grip of the dentalappliance such as an aligner in the direction of the desired movement.Generally, the attachments operate to provide “bumps” or “undercuts” onthe vertical surface of the tooth which otherwise would be difficult forthe dental appliance to grip.

Existing approaches to achieve the desired movement of the tooth includefabrication of dental appliances from the planned next or n+1 positionand placed over the teeth during the current or n position of thetreatment stage. Typically, it is assumed that the forces and torquesgenerated by the deformation of the dental appliance or portions thereof(resulting from the difference in the teeth position used for the dentalappliance fabrication and the position of the teeth it has beenpositioned over) will cause the teeth to move into the planned nextposition in the treatment stage.

In practice, however, the generated forces and torques may not beoriented in the direction of the intended tooth movement, whether or notdental attachments are used in the treatment. Further, the current toothmovement may be programmed or configured only for the tooth crown, andnot factoring into the root of the tooth or other anatomical structures.The root of the tooth or other anatomical structures may hinder thecrown movement and render the center of resistance down in the toothbone socket. Generally, the undesirable torque to the center ofresistance as a result of the force on the tooth crown may not be easilycounter balanced. Moreover, as the teeth move during the course of thetreatment, the deformation of the dental appliance diminishes, renderingthe applied forces to diminish as well.

SUMMARY OF THE INVENTION

In one embodiment, method and apparatus including establishing aninitial position of a tooth, determining a target position of the toothin a treatment plan, calculating a movement vector associated with thetooth movement from the initial position to the target position,determining a plurality of components corresponding to the movementvector, and determining a corresponding one or more positions of arespective one or more attachment devices relative to a surface plane ofthe tooth such that the one or more attachment devices engages with adental appliance, are provided.

Attachment as used herein may be any form of material that may beattached to the tooth whether preformed, formed using a template or inan amorphous form that is attached to the surface of the tooth. It canbe disposed on the tooth surface using an adhesive material, or theadhesive material itself may be disposed on the surface of the tooth asattachment.

These and other features and advantages of the present invention will beunderstood upon consideration of the following detailed description ofthe invention and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows one exemplary dental data mining system;

FIG. 1B shows an analysis of the performance of one or more dentalappliances;

FIG. 1C shows various Movement Type data used in one embodiment of thedata mining system;

FIG. 1D shows an analysis of the performance of one or more dentalappliances;

FIGS. 1L-1F show various embodiments of a clusterizer to generatetreatment plans;

FIG. 2A is a flowchart of a process of specifying a course of treatmentincluding a subprocess for calculating aligner shapes in accordance withthe invention;

FIG. 2B is a flowchart of a process for calculating aligner shapes;

FIG. 3 is a flowchart of a subprocess for creating finite elementmodels;

FIG. 4 is a flowchart of a subprocess for computing aligner changes;

FIG. 5A is a flowchart of a subprocess for calculating changes inaligner shape;

FIG. 5B is a flowchart of a subprocess for calculating changes inaligner shape;

FIG. 5C is a flowchart of a subprocess for calculating changes inaligner shape;

FIG. 5D is a schematic illustrating the operation of the subprocess ofFIG. 5B;

FIG. 6 is a flowchart of a process for computing shapes for sets ofaligners;

FIG. 7 is an exemplary diagram of a statistical root model;

FIG. 8 shows exemplary diagrams of root modeling;

FIG. 9 show exemplary diagrams of CT scan of teeth;

FIG. 10 shows an exemplary user interface showing teeth;

FIGS. 11A-11B illustrate an initial tooth position with a positioneddental appliance, and a resulting undesirable force vector,respectively;

FIGS. 11C-11D illustrate a relief addition to the dental appliance tocounteract the undesirable force vector around the tooth, and theresulting desired application of the predetermined force on the tooth bythe dental appliance, respectively;

FIG. 12 illustrates a modified dental appliance geometry including anadditional shape modification to remove a gap between the dentalappliance and the tooth;

FIG. 13 illustrates dental appliance shape geometry configuration basedon sweep geometry of the treatment plan for a tooth;

FIGS. 14A-14B illustrate dental attachment positioning for toothrotation;

FIG. 15 illustrates dental attachment positioning for tooth inclination;

FIG. 16 illustrates dental attachment positioning for tooth angulation;

FIGS. 17A-17B illustrate dental attachment positioning for buccaltranslation and lingual translation, respectively;

FIGS. 18A-18B illustrate dental attachment positioning for mesial anddistal translation, respectively;

FIGS. 19A-19B illustrate dental attachment positioning for extrusion andintrusion, respectively;

FIG. 20 illustrates a complementary engagement of the dental applianceand the attachment;

FIG. 21 is a flowchart illustrating the optimized shape geometry of thedental appliance;

FIG. 22 is a flowchart illustrating the dental attachment positioning;

FIG. 23 is a flowchart illustrating a method of moving teeth apredetermined distance and direction based on computing active toothsurfaces;

FIG. 24 is a flowchart illustrating a method of determining if anattachment is required to obtain sufficient active surface area of atooth;

FIG. 25 is a flowchart of a process for calculating a dental applianceshape;

FIG. 26 shows the trajectories of crown points from a first stage to asecond stage;

FIG. 27 shows the active surface and resistance surface of a tooth;

FIG. 28 demonstrates the increase in active surface of a tooth by theaddition of an attachment; and

FIG. 29 shows a cross-section of a tooth with an attachment and alignerwith a ridge to match the attachment.

DETAILED DESCRIPTION

Digital treatment plans are now possible with 3-dimensional orthodontictreatment planning tools such as software from Align Technology, Inc. orother software available from eModels and OrthoCAD, among others. Thesetechnologies allow the clinician to use the actual patient's dentitionas a starting point for customizing the treatment plan. The softwaretechnology available from Align Technology, Inc., uses apatient-specific digital model to plot a treatment plan, and then use ascan of the achieved or actual treatment outcome to assess the degree ofsuccess of the outcome as compared to the original digital treatmentplan as discussed in U.S. patent application Ser. No. 10/640,439, filedAug. 21, 2003 and U.S. patent application Ser. No. 10/225,889 filed Aug.22, 2002. The problem with the digital treatment plan and outcomeassessment is the abundance of data and the lack of standards andefficient methodology by which to assess “treatment success” at anindividual patient level. To analyze the information, a dental datamining system is used.

FIG. 1A shows one exemplary dental data mining system. In this system,dental treatment and outcome data sets 1 are stored in a database orinformation warehouse 2. The data is extracted by data mining software 3that generates results 4. The data mining software can interrogate theinformation captured and/or updated in the database 2 and can generatean output data stream correlating a patient tooth problem with a dentalappliance solution. Note that the output of the data mining software canbe most advantageously, self-reflexively, fed as a subsequent input toat least the database and the data mining correlation algorithm.

The result of the data mining system of FIG. 1A is used for definingappliance configurations or changes to appliance configurations forincrementally moving teeth. The tooth movements will be those normallyassociated with orthodontic treatment, including translation in allthree orthogonal directions, rotation of the tooth centerline in the twoorthogonal directions with rotational axes perpendicular to a verticalcenterline (“root angulation” and “torque”), as well as rotation of thetooth centerline in the orthodontic direction with an axis parallel tothe vertical centerline (“pure rotation”).

In one embodiment, the data mining system captures the 3-D treatmentplanned movement, the start position and the final achieved dentalposition. The system compares the outcome to the plan, and the outcomecan be achieved using any treatment methodology, including removableappliances as well as fixed appliances, such as orthodontic brackets andwires, or even other dental treatment, such as comparing achieved toplan for orthognathic surgery, periodontics, and restorative, amongothers.

In one embodiment, a teeth superimposition tool is used to matchtreatment files of each arch scan. The refinement (subsequent progress)scan is superimposed over the initial one to arrive at a match basedupon tooth anatomy and tooth coordinate system. After teeth in the twoarches are matched, the superimposition tool asks for a reference inorder to relate the upper arch to the lower arch. When the option“statistical filtering” is selected, the superimposition tool measuresthe amount of movement for each tooth by first eliminating as referencethe ones that move (determined by the difference in position between thecurrent stage and the previous one) more than one standard deviationeither above or below the mean of movement of all teeth. The remainingteeth are then selected as reference to measure movement of each tooth.

FIG. 1B shows an analysis of the performance of one or more dentalappliances. “Achieved” movement is plotted against “Goal” movement inscatter graphs, and trend lines are generated. Scatter graphs are shownto demonstrate where all “scattered” data points are, and trend linesare generated to show the performance of the dental appliances. In oneembodiment, trend lines are selected to be linear (they can becurvilinear); thus trend lines present as the “best fit” straight linesfor all “scattered” data. The performance of the Aligners is representedas the slope of a trend line. The Y axis intercept models the incidentalmovement that occurs when wearing the Aligners. Predictability ismeasured by R² that is obtained from a regression computation of“Achieved” and “Goal” data.

FIG. 1C shows various Movement Type data used in one embodiment of thedata mining system. Exemplary data sets cover Expansion/Constriction(±Translation), Mesialization/Distalization (±Translation), Intrusion(−Z Translation), Extrusion (+Z Translation), Tip/Angulation (XRotation), Torque/Inclination (Y Rotation), and Pure Rotation (ZRotation).

FIG. 1D shows an analysis of the performance of one or more dentalappliances. For the type of motion illustrated by FIG. 1D, the motionachieved is about 85% of targeted motion for that particular set ofdata.

As illustrated saliently in FIG. 1D, actual tooth movement generallylags targeted tooth movement at many stages. In the case of treatmentwith sequences of polymer appliances, such lags play an important rolein treatment design, because both tooth movement and such negativeoutcomes as patient discomfort vary positively with the extent of thediscrepancies.

In one embodiment, clinical parameters in steps such as 170 (FIG. 2A)and 232 (FIG. 2B) are made more precise by allowing for the statisticaldeviation of targeted from actual tooth position. For example, asubsequent movement target might be reduced because of a largecalculated probability of currently targeted tooth movement not havingbeen achieved adequately, with the result that there is a highprobability the subsequent movement stage will need to complete workintended for an earlier stage. Similarly, targeted movement mightovershoot desired positions especially in earlier stages so thatexpected actual movement is better controlled. This embodimentsacrifices the goal of minimizing round trip time in favor of achievinga higher probability of targeted end-stage outcome. This methodology isaccomplished within treatment plans specific to clusters of similarpatient cases.

Table 1 shows grouping of teeth in one embodiment. The sign conventionof tooth movements is indicated in Table 2. Different tooth movements ofthe selected 60 arches were demonstrated in Table 3 with performancesorted by descending order. The appliance performance can be broken into4 separate groups: high (79-85%), average (60-68%), below average(52-55%), and inadequate (24-47%). Table 4 shows ranking of movementpredictability. Predictability is broken into 3 groups: highlypredictable (0.76-0.82), predictable (0.43-0.63) and unpredictable(0.10-0.30). For the particular set of data, for example, the findingsare as follows:

Incisor intrusion and anterior intrusion performance are high. The rangefor incisor intrusion is about 1.7 mm, and for anterior intrusion isabout 1.7 mm. These movements are highly predictable.

Canine intrusion, incisor torque, incisor rotation and anterior torqueperformance are average. The range for canine intrusion is about 1.3 mm,for incisor torque is about 34 degrees, for incisor rotation is about 69degrees, and for anterior torque is about 34 degrees. These movementsare either predictable or highly predictable.

Bicuspid tipping, bicuspid mesialization, molar rotation, and posteriorexpansion performance are below average. The range for bicuspidmesialization is about 1 millimeter, for bicuspid tipping is about 19degrees, for molar rotation is about 27 degrees and for posteriorexpansion is about 2.8 millimeters. Bicuspid tipping and mesializationare unpredictable, whereas the rest are predictable movements.

Anterior and incisor extrusion, round teeth and bicuspid rotation,canine tipping, molar distalization, and posterior torque performanceare inadequate. The range of anterior extrusion is about 1.7millimeters, for incisor extrusion is about 1.5 mm, for round teethrotation is about 67 degrees, for bicuspid rotation is about 63 degrees,for canine tipping is about 26 degrees, for molar distalization is about2 millimeters, and for posterior torque is about 43 degrees. All areunpredictable movements except bicuspid rotation which is predictable(but lower in yield in terms of performance).

TABLE 1 Studied groups of teeth Teeth Incisors #7, 8, 9, 10, 23, 24, 25,26 Canines #6, 11, 22, 27 Bicuspids #4, 5, 12, 13, 20, 21, 28, 29 Molars#2, 3, 14, 15, 18, 19, 30, 31 Anteriors #6, 7, 8, 9, 10, 11, 22, 23, 24,25, 26, 27 Posteriors #2, 3, 4, 5, 12, 13, 14, 15, 18, 19, 20, 21, 28,29, 30, 31 Round #4, 5, 6, 11, 12, 13, 20, 21, 22, 27, 28, 29

TABLE 2 Sign convention of tooth movements Type of Movement Xtranslation (−) is lingual (+) is buccal (Expansion/ Constriction) Xrotation (Tipping) Upper & Lower (−) is distal (+) is mesial rightquadrants Upper & Lower (−) is mesial (+) is distal left quadrants Ytranslation (Mesialization/Distalization) Upper left & Lower (−) isdistal (+) is mesial right quadrants Upper right & Lower (−) is mesial(+) is distal left quadrants Y rotation (−) is lingual crown (+) isbuccal crown (Torquing) Z translation (−) is intrusion (+) is extrusion(Intrusion/Extrusion) Z rotation (−) is clockwise (+) iscounterclockwise (Pure Rotation)

TABLE 3 Ranking of Performance Index of movement Performance SidePredicta- Group Movement Model Index Effect bility Incisor IntrusionLinear 85% 0.03 0.82 Anterior Intrusion Linear 79% 0.03 0.76 CanineIntrusion Linear 68% −0.10 0.43 Incisor Torque Linear 67% 0.21 0.63Anterior Torque Linear 62% 0.15 0.56 Incisor Rotation Linear 61% −0.090.76 Bicuspid Tipping Linear 55% 0.35 0.27 Molar Rotation Linear 52%0.11 0.58 Posterior Expansion Linear 52% 0.11 0.48 BicuspidMesialization Linear 52% 0.00 0.30 Bicuspid Rotation Linear 47% 0.280.63 Molar Distalization Linear 43% 0.02 0.20 Canine Tipping Linear 42%0.10 0.28 Posterior Torque Linear 42% 1.50 0.28 Round Rotation Linear39% −0.14 0.27 Anterior Extrusion Linear 29% −0.02 0.13 IncisorExtrusion Linear 24% 0.02 0.10

TABLE 4 Ranking of movement predictability Performance Side Predicta-Group Movement Model Index Effect bility Incisor Intrusion Linear 85%0.03 0.82 Anterior Intrusion Linear 79% 0.03 0.76 Incisor RotationLinear 61% −0.09 0.76 Incisor Torque Linear 67% 0.21 0.63 BicuspidRotation Linear 47% 0.28 0.63 Molar Rotation Linear 52% 0.11 0.58Anterior Torque Linear 62% 0.15 0.56 Posterior Expansion Linear 52% 0.110.48 Canine Intrusion Linear 68% −0.10 0.43 Bicuspid MesializationLinear 52% 0.00 0.30 Canine Tipping Linear 42% 0.10 0.28 PosteriorTorque Linear 42% 1.50 0.28 Bicuspid Tipping Linear 55% 0.35 0.27 RoundRotation Linear 39% −0.14 0.27 Molar Distalization Linear 43% 0.02 0.20Anterior Extrusion Linear 29% −0.02 0.13 Incisor Extrusion Linear 24%0.02 0.10

In one embodiment, data driven analyzers may be applied. These datadriven analyzers may incorporate a number of models such as parametricstatistical models, non-parametric statistical models, clusteringmodels, nearest neighbor models, regression methods, and engineered(artificial) neural networks. Prior to operation, data driven analyzersor models are built using one or more training sessions. The data usedto build the analyzer or model in these sessions are typically referredto as training data. As data driven analyzers are developed by examiningonly training examples, the selection of the training data cansignificantly affect the accuracy and the learning speed of the datadriven analyzer. One approach used heretofore generates a separate dataset referred to as a test set for training purposes. The test set isused to avoid overfitting the model or analyzer to the training data.Overfitting refers to the situation where the analyzer has memorized thetraining data so well that it fails to fit or categorize unseen data.Typically, during the construction of the analyzer or model, theanalyzer's performance is tested against the test set. The selection ofthe analyzer or model parameters is performed iteratively until theperformance of the analyzer in classifying the test set reaches anoptimal point. At this point, the training process is completed. Analternative to using an independent training and test set is to use amethodology called cross-validation. Cross-validation can be used todetermine parameter values for a parametric analyzer or model for anon-parametric analyzer. In cross-validation, a single training data setis selected. Next, a number of different analyzers or models are builtby presenting different parts of the training data as test sets to theanalyzers in an iterative process. The parameter or model structure isthen determined on the basis of the combined performance of all modelsor analyzers. Under the cross-validation approach, the analyzer or modelis typically retrained with data using the determined optimal modelstructure.

In one embodiment, the data mining software 3 (FIG. 1A) can be a“spider” or “crawler” to grab data on the database 2 (FIG. 1A) forindexing. In one embodiment, clustering operations are performed todetect patterns in the data. In another embodiment, a neural network isused to recognize each pattern as the neural network is quite robust atrecognizing dental treatment patterns. Once the treatment features havebeen characterized, the neural network then compares the input dentalinformation with stored templates of treatment vocabulary known by theneural network recognizer, among others. The recognition models caninclude a Hidden Markov Model (HMM), a dynamic programming model, aneural network, a fuzzy logic, or a template matcher, among others.These models may be used singly or in combination.

Dynamic programming considers all possible paths of M “frames” through Npoints, subject to specified costs for making transitions from any pointi to any given frame k to any point j at the next frame k+1. Because thebest path from the current point to the next point is independent ofwhat happens beyond that point, the minimum total cost [i(k), j(k+1)] ofa path through i(k) ending at j(k+1) is the cost of the transitionitself plus the cost of the minimum path to i(k). Preferably, the valuesof the predecessor paths can be kept in an M×N array, and theaccumulated cost kept in a 2×N array to contain the accumulated costs ofthe possible immediately preceding column and the current column.However, this method requires significant computing resources.

Dynamic programming requires a tremendous amount of computation. For therecognizer to find the optimal time alignment between a sequence offrames and a sequence of node models, it must compare most framesagainst a plurality of node models. One method of reducing the amount ofcomputation required for dynamic programming is to use pruning. Pruningterminates the dynamic programming of a given portion of dentaltreatment information against a given treatment model if the partialprobability score for that comparison drops below a given threshold.This greatly reduces computation.

Considered to be a generalization of dynamic programming, a hiddenMarkov model is used in the preferred embodiment to evaluate theprobability of occurrence of a sequence of observations O(1), O(2),O(t), . . . , O(T), where each observation O(t) may be either a discretesymbol under the VQ approach or a continuous vector. The sequence ofobservations may be modeled as a probabilistic function of an underlyingMarkov chain having state transitions that are not directly observable.

In the preferred embodiment, the Markov model is used to modelprobabilities for sequences of treatment observations. The transitionsbetween states are represented by a transition matrix A=[a(i,j)]. Eacha(i,j) term of the transition matrix is the probability of making atransition to state j given that the model is in state i. The outputsymbol probability of the model is represented by a set of functionsB=[b(j), where the b(j) term of the output symbol matrix is the functionthat when evaluated on a specified value O(t) returns the probability ofoutputting observation O(t), given that the model is in state j. Thefirst state is always constrained to be the initial state for the firsttime frame of the Markov chain, only a prescribed set of left to rightstate transitions are possible. A predetermined final state is definedfrom which transitions to other states cannot occur.

In one embodiment, transitions are restricted to reentry of a state orentry to one of the next two states. Such transitions are defined in themodel as transition probabilities. For example, a treatment patterncurrently having a frame of feature signals in state 2 has a probabilityof reentering state 2 of a(2,2), a probability a(2,3) of entering state3 and a probability of a(2,4)=1-a(2,2)-a(2,3) of entering state 4. Theprobability a(2, 1) of entering state 1 or the probability a(2,5) ofentering state 5 is zero and the sum of the probabilities a(2, 1)through a(2,5) is one. Although the preferred embodiment restricts theflow graphs to the present state or to the next two states, one skilledin the art can build an HMM model with more flexible transitionrestrictions, although the sum of all the probabilities of transitioningfrom any state must still add up to one.

In each state j of the model, the current feature frame may beidentified with one of a set of predefined output symbols or may belabeled probabilistically. In this case, the output symbol probabilityb(j) (O(t)) corresponds to the probability assigned by the model thatthe feature frame symbol is O(t). The model arrangement is a matrixA=[a(i,j)] of transition probabilities and a technique of computingB=[b(j) (O(t))].

In one embodiment, the Markov model is formed for a reference patternfrom a plurality of sequences of training patterns and the output symbolprobabilities are multivariate Gaussian function probability densities.The dental treatment information traverses through the featureextractor. During learning, the resulting feature vector series isprocessed by a parameter estimator, whose output is provided to thehidden Markov model. The hidden Markov model is used to derive a set ofreference pattern templates, each template representative of anidentified pattern in a vocabulary set of reference treatment patterns.The Markov model reference templates are next utilized to classify asequence of observations into one of the reference patterns based on theprobability of generating the observations from each Markov modelreference pattern template. During recognition, the unknown pattern canthen be identified as the reference pattern with the highest probabilityin the likelihood calculator.

The HMM template has a number of states, each having a discrete value.However, as treatment pattern features may have a dynamic pattern incontrast to a single value, the addition of a neural network at thefront end of the HMM in an embodiment provides the capability ofrepresenting states with dynamic values. The input layer of the neuralnetwork comprises input neurons. The outputs of the input layer aredistributed to all neurons in the middle layer. Similarly, the outputsof the middle layer are distributed to all output neurons, which outputneurons correspond one-to one with internal states of the HMM. However,each output has transition probabilities to itself or to other outputs,thus forming a modified HMM. Each state of the thus formed HMM iscapable of responding to a particular dynamic signal, resulting in amore robust HMM. Alternatively, the neural network can be used alonewithout resorting to the transition probabilities of the HMMarchitecture.

The output streams or results 4 of FIG. 1A are used as feedback inimproving dental appliance design and/or usage by doctors. For example,the data mining results can be used to evaluate performance based onstaging approaches, to compare appliance performance indices based ontreatment approaches, and to evaluate performance comparing differentattachment shapes and positions on teeth.

The ability to study tooth-specific efficacy and product performance forlarge clusters of treatment outcomes enables statistically significantcomparisons to be made between two or more populations of cases. In theevent that the two clusters studied contain differences in treatmentapproach, appliance design, or manufacturing protocol, the differencesseen in the performance of the product as exhibited by the data output,can be attributed to the approach, design, or manufacturing protocol.The end result is a feedback mechanism that enables either the clinicianor the manufacturer the ability to optimize the product design and usagebased on performance data from a significantly large sample size usingobjective measurable data.

The theory of orthodontic treatment is not universally agreed upon, andactual treatment and outcomes are subject to additional uncertainties ofmeasurement of patient variables, of relationships to unmeasured patientvariables, as well as of varying patient compliance. As a result,different clinicians might prefer different treatment plans for a singlepatient. Thus, a single treatment plan may not be accepted by everyclinician since there is no universally accepted “correct” treatmentplan.

The next few embodiments allow greater clinician satisfaction andgreater patient satisfaction by tailoring treatment parameters topreferences of clinicians. The system detects differences in treatmentpreferences by statistical observation of the treatment histories ofclinicians. For example, clinicians vary in how likely they would be toperform bicuspid extraction in cases with comparable crowding. Even whenthere is not a sufficient record of past treatments for a givenclinician, clustering may be performed on other predictor variables suchas geographical location, variables related to training, or size andnature of practice, to observe statistically significant differences intreatment parameters.

Data mining can discover statistically significant patterns of differenttreatment outcomes achieved by different clinicians for comparablepatients. For example, patient cases clustered together might havesystematically fewer complications with one clinician as compared toanother. Such a difference detected by the data mining tool might beused as a flag for feedback to the more poorly performing clinician aswell as a flag for solicitation of treatment differences used by thebetter performing clinician.

In one embodiment, clustering techniques are used with previouslycompleted cases to categorize treatment complications and outcomes.Probability models of risk are then built within each cluster. New casesare then allocated to the same clusters based on similarity ofpre-treatment variables. The risks within each cluster of patients withcompleted treatments are then used with new cases to predict treatmentoutcomes and risks of complications. High-risk patients are then flaggedfor special attention, possibly including additional steps in treatmentplan or additional clinical intervention.

In another embodiment, practitioners are clustered into groups byobserved clinician treatment preferences, and treatment parameters areadjusted within each group to coincide more closely with observedtreatment preferences. Practitioners without observed histories are thenassigned to groups based on similarity of known variables to thosewithin clusters with known treatment histories.

FIG. 1E shows an exemplary process for clusterizing practices. First,the process clusterizes treatment practice based on clinician treatmenthistory such as treatment preferences, outcomes, and demographic andpractice variables (20). Next, the system models preferred clinicalconstraints within each cluster (22). Next, the system assignsclinicians without treatment history to clusters in 20 based ondemographic and practice variables (24). In one embodiment, the systemperforms process 100 (see FIG. 2A) separately within each cluster, usingcluster-specific clinical constraints (26). Additionally, the systemupdates clusters and cluster assignments as new treatment and outcomedata arrives (28).

FIG. 1F shows another embodiment of a data mining system to generateproposed treatments. First, the system identifies/clusterizes patienthistories having detailed follow-up (such as multiple high-resolutionscans), based on detailed follow-up data, diagnosis, treatmentparameters and outcomes, and demographic variables (40). Within eachcluster, the system models discrepancies between intended position andactual positions obtained from follow-up data (42). Further, within eachcluster, the system models risk for special undesirable outcomes (44).At a second tier of clustering, patient histories with less detailedfollow-up data are clusterized based on available variables. Thesecond-tier clustering is partial enough that each of the larger numberof second tier clusters can either be assigned to clusters calculated in40 or else considered a new cluster (46). The system refines step 42models with additional records from step 46 clusters (48). It can alsorefine step 44 models with additional records from step 48 clusters(50). At a third tier of clustering, the system then assigns newpatients to step 46 clusters based on diagnosis, demographic, andinitial physical (52). Within each step 52 cluster, the system modelsexpected discrepancies between intended position and actual positions(54). From step 54, the system uses revised expected positioninformation where relevant (including 232 and 250, FIG. 2B) (67).Additionally, within each step 52 cluster, the system models risk forundesirable outcomes (56). From step 56, the system also flags casesthat require special attention and clinical constraints (as in 204 and160, FIGS. 2B and 2A) (69). The process then customizes treatment planto each step 52 cluster (58). Next, the system iteratively collects data(61) and loops back to identify/clusterize patient histories (40).Additionally, clusters can be revised and reassigned (63). The systemalso continually identifies clusters without good representation foradditional follow-up analysis (65).

In clinical treatment settings, it is not cost-effective to obtain orprocess the full high-resolution data possible at every stage of toothmovement. For example:

-   -   Patients may use several appliances between visits to        clinicians.    -   A given patient may submit only one set of tooth impressions.    -   Radiation concerns may limit the number of CT or X-Ray scans        used.    -   Clinicians generally do not have the time to report detailed        spatial information on each tooth at each visit.

Due to these and other limitations, treatment planning is necessarilymade based on partial information.

In one embodiment, missing information is approximated substantially bymatching predictive characteristics between patients and arepresentative sample for which detailed follow-up information iscollected. In this case, patients are flagged based on poorlyanticipated treatment outcomes for requests for follow-up information,such as collection and analysis of additional sets of tooth impressions.Resulting information is then used to refine patient clusters andtreatment of patients later assigned to the clusters.

In general, patient data is scanned and the data is analyzed using thedata mining system described above. A treatment plan is proposed by thesystem for the dental practitioner to approve. The dental practitionercan accept or request modifications to the treatment plan. Once thetreatment plan is approved, manufacturing of appliance(s) can begin.

FIG. 2A illustrates the general flow of an exemplary process 100 fordefining and generating repositioning appliances for orthodontictreatment of a patient. The process 100 includes the methods, and issuitable for the apparatus, of the present invention, as will bedescribed. The computational steps of the process are advantageouslyimplemented as computer program modules for execution on one or moreconventional digital computers.

As an initial step, a mold or a scan of patient's teeth or mouth tissueis acquired (110). This step generally involves taking casts of thepatient's teeth and gums, and may in addition or alternately involvetaking wax bites, direct contact scanning, x-ray imaging, tomographicimaging, sonographic imaging, and other techniques for obtaininginformation about the position and structure of the teeth, jaws, gumsand other orthodontically relevant tissue. From the data so obtained, adigital data set is derived that represents the initial (that is,pretreatment) arrangement of the patient's teeth and other tissues.

The initial digital data set, which may include both raw data fromscanning operations and data representing surface models derived fromthe raw data, is processed to segment the tissue constituents from eachother (step 120). In particular, in this step, data structures thatdigitally represent individual tooth crowns are produced.Advantageously, digital models of entire teeth are produced, includingmeasured or extrapolated hidden surfaces and root structures as well assurrounding bone and soft tissue.

The desired final position of the teeth—that is, the desired andintended end result of orthodontic treatment—can be received from aclinician in the form of a prescription, can be calculated from basicorthodontic principles, or can be extrapolated computationally from aclinical prescription (step 130). With a specification of the desiredfinal positions of the teeth and a digital representation of the teeththemselves, the final position and surface geometry of each tooth can bespecified (step 140) to form a complete model of the teeth at thedesired end of treatment. Generally, in this step, the position of everytooth is specified. The result of this step is a set of digital datastructures that represents an orthodontically correct repositioning ofthe modeled teeth relative to presumed-stable tissue. The teeth andtissue are both represented as digital data.

Having both a beginning position and a final position for each tooth,the process next defines a tooth path for the motion of each tooth. Inone embodiment, the tooth paths are optimized in the aggregate so thatthe teeth are moved in the quickest fashion with the least amount ofround-tripping to bring the teeth from their initial positions to theirdesired final positions. (Round-tripping is any motion of a tooth in anydirection other than directly toward the desired final position.Round-tripping is sometimes necessary to allow teeth to move past eachother.) The tooth paths are segmented. The segments are calculated sothat each tooth's motion within a segment stays within threshold limitsof linear and rotational translation. In this way, the end points ofeach path segment can constitute a clinically viable repositioning, andthe aggregate of segment end points constitute a clinically viablesequence of tooth positions, so that moving from one point to the nextin the sequence does not result in a collision of teeth.

The threshold limits of linear and rotational translation areinitialized, in one implementation, with default values based on thenature of the appliance to be used. More individually tailored limitvalues can be calculated using patient-specific data. The limit valuescan also be updated based on the result of an appliance-calculation(step 170, described later), which may determine that at one or morepoints along one or more tooth paths, the forces that can be generatedby the appliance on the then-existing configuration of teeth and tissueis incapable of effecting the repositioning that is represented by oneor more tooth path segments. With this information, the subprocessdefining segmented paths (step 150) can recalculate the paths or theaffected subpaths.

At various stages of the process, and in particular after the segmentedpaths have been defined, the process can, and generally will, interactwith a clinician responsible for the treatment of the patient (step160). Clinician interaction can be implemented using a client processprogrammed to receive tooth positions and models, as well as pathinformation from a server computer or process in which other steps ofprocess 100 are implemented. The client process is advantageouslyprogrammed to allow the clinician to display an animation of thepositions and paths and to allow the clinician to reset the finalpositions of one or more of the teeth and to specify constraints to beapplied to the segmented paths. If the clinician makes any such changes,the subprocess of defining segmented paths (step 150) is performedagain.

The segmented tooth paths and associated tooth position data are used tocalculate clinically acceptable appliance configurations (or successivechanges in appliance configuration) that will move the teeth on thedefined treatment path in the steps specified by the path segments (step170). Each appliance configuration represents a step along the treatmentpath for the patient. The steps are defined and calculated so that eachdiscrete position can follow by straight-line tooth movement or simplerotation from the tooth positions achieved by the preceding discretestep and so that the amount of repositioning required at each stepinvolves an orthodontically optimal amount of force on the patient'sdentition. As with the path definition step, this appliance calculationstep can include interactions and even iterative interactions with theclinician (step 160). The operation of a process step 200 implementingthis step will be described more fully below.

Having calculated appliance definitions, the process 100 can proceed tothe manufacturing step (step 180) in which appliances defined by theprocess are manufactured, or electronic or printed information isproduced that can be used by a manual or automated process to defineappliance configurations or changes to appliance configurations.

FIG. 2B illustrates a process 200 implementing the appliance-calculationstep (FIG. 2A, step 170) for polymeric shell aligners of the kinddescribed in above-mentioned U.S. Pat. No. 5,975,893. Inputs to theprocess include an initial aligner shape 202, various control parameters204, and a desired end configuration for the teeth at the end of thecurrent treatment path segment 206. Other inputs include digital modelsof the teeth in position in the jaw, models of the jaw tissue, andspecifications of an initial aligner shape and of the aligner material.Using the input data, the process creates a finite element model of thealigner, teeth and tissue, with the aligner in place on the teeth (step210). Next, the process applies a finite element analysis to thecomposite finite element model of aligner, teeth and tissue (step 220).The analysis runs until an exit condition is reached, at which time theprocess evaluates whether the teeth have reached the desired endposition for the current path segment, or a position sufficiently closeto the desired end position (step 230). If an acceptable end position isnot reached by the teeth, the process calculates a new candidate alignershape (step 240). If an acceptable end position is reached, the motionsof the teeth calculated by the finite elements analysis are evaluated todetermine whether they are orthodontically acceptable (step 232). Ifthey are not, the process also proceeds to calculate a new candidatealigner shape (step 240). If the motions are orthodontically acceptableand the teeth have reached an acceptable position, the current alignershape is compared to the previously calculated aligner shapes. If thecurrent shape is the best solution so far (decision step 250), it issaved as the best candidate so far (step 260). If not, it is saved in anoptional step as a possible intermediate result (step 252). If thecurrent aligner shape is the best candidate so far, the processdetermines whether it is good enough to be accepted (decision step 270).If it is, the process exits. Otherwise, the process continues andcalculates another candidate shape (step 240) for analysis.

The finite element models can be created using computer programapplication software available from a variety of vendors. For creatingsolid geometry models, computer aided engineering (CAE) or computeraided design (CAD) programs can be used, such as the AutoCAD® softwareproducts available from Autodesk, Inc., of San Rafael, Calif. Forcreating finite element models and analyzing them, program products froma number of vendors can be used, including the PolyFEM product availablefrom CADSI of Coralville, Iowa, the Pro/Mechanica simulation softwareavailable from Parametric Technology Corporation of Waltham, Mass., theI-DEAS design software products available from Structural DynamicsResearch Corporation (SDRC) of Cincinnati, Ohio, and the MSC/NASTRANproduct available from MacNeal-Schwendler Corporation of Los Angeles,Calif.

FIG. 3 shows a process 300 of creating a finite element model that canbe used to perform step 210 of the process 200 (FIG. 2). Input to themodel creation process 300 includes input data 302 describing the teethand tissues and input data 304 describing the aligner. The input datadescribing the teeth 302 include the digital models of the teeth;digital models of rigid tissue structures, if available; shape andviscosity specifications for a highly viscous fluid modeling thesubstrate tissue in which the teeth are embedded and to which the teethare connected, in the absence of specific models of those tissues; andboundary conditions specifying the immovable boundaries of the modelelements. In one implementation, the model elements include only modelsof the teeth, a model of a highly viscous embedding substrate fluid, andboundary conditions that define, in effect, a rigid container in whichthe modeled fluid is held. Note that fluid characteristics may differ bypatient clusters, for example as a function of age.

A finite element model of the initial configuration of the teeth andtissue is created (step 310) and optionally cached for reuse in lateriterations of the process (step 320). As was done with the teeth andtissue, a finite element model is created of the polymeric shell aligner(step 330). The input data for this model includes data specifying thematerial of which the aligner is made and the shape of the aligner (datainput 304).

The model aligner is then computationally manipulated to place it overthe modeled teeth in the model jaw to create a composite model of anin-place aligner (step 340). Optionally, the forces required to deformthe aligner to fit over the teeth, including any hardware attached tothe teeth, are computed and used as a figure of merit in measuring theacceptability of the particular aligner configuration. Optionally, thetooth positions used are as estimated from a probabilistic model basedon prior treatment steps and other patient information. In a simpleralternative, however, the aligner deformation is modeled by applyingenough force to its insides to make it large enough to fit over theteeth, placing the model aligner over the model teeth in the compositemodel, setting the conditions of the model teeth and tissue to beinfinitely rigid, and allowing the model aligner to relax into positionover the fixed teeth. The surfaces of the aligner and the teeth aremodeled to interact without friction at this stage, so that the alignermodel achieves the correct initial configuration over the model teethbefore finite element analysis is begun to find a solution to thecomposite model and compute the movement of the teeth under theinfluence of the distorted aligner.

FIG. 4 shows a process 400 for calculating the shape of a next alignerthat can be used in the aligner calculations, step 240 of process 200(FIG. 2B). A variety of inputs are used to calculate the next candidatealigner shape. These include inputs 402 of data generated by the finiteelement analysis solution of the composite model and data 404 defined bythe current tooth path. The data 402 derived from the finite elementanalysis includes the amount of real elapsed time over which thesimulated repositioning of the teeth took place; the actual end toothpositions calculated by the analysis; the maximum linear and torsionalforce applied to each tooth; the maximum linear and angular velocity ofeach tooth. From the input path information, the input data 404 includesthe initial tooth positions for the current path segment, the desiredtooth positions at the end of the current path segment, the maximumallowable displacement velocity for each tooth, and the maximumallowable force of each kind for each tooth.

If a previously evaluated aligner was found to violate one or moreconstraints, additional input data 406 can optionally be used by theprocess 400. This data 406 can include information identifying theconstraints violated by, and any identified suboptimal performance of,the previously evaluated aligner. Additionally, input data 408 relatingto constraints violated by, and suboptimal performance of previousdental devices can be used by the process 400.

Having received the initial input data (step 420), the process iteratesover the movable teeth in the model. (Some of the teeth may beidentified as, and constrained to be, immobile.) If the end position anddynamics of motion of the currently selected tooth by the previouslyselected aligner is acceptable (“yes” branch of decision step 440), theprocess continues by selecting for consideration a next tooth (step 430)until all teeth have been considered (“done” branch from step 430 tostep 470). Otherwise (“no” branch from step 440), a change in thealigner is calculated in the region of the currently selected tooth(step 450). The process then moves back to select the next current tooth(step 430) as has been described.

When all of the teeth have been considered, the aggregate changes madeto the aligner are evaluated against previously defined constraints(step 470), examples of which have already been mentioned. Constraintscan be defined with reference to a variety of further considerations,such as manufacturability. For example, constraints can be defined toset a maximum or minimum thickness of the aligner material, or to set amaximum or minimum coverage of the aligner over the crowns of the teeth.If the aligner constraints are satisfied, the changes are applied todefine a new aligner shape (step 490). Otherwise, the changes to thealigner are revised to satisfy the constraints (step 480), and therevised changes are applied to define the new aligner shape (step 490).

FIG. 5A illustrates one implementation of the step of computing analigner change in a region of a current tooth (step 450). In thisimplementation, a rule-based inference engine 456 is used to process theinput data previously described (input 454) and a set of rules 452 a-452n in a rule base of rules 452. The inference engine 456 and the rules452 define a production system which, when applied to the factual inputdata, produces a set of output conclusions that specify the changes tobe made to the aligner in the region of the current tooth (output 458).

Rules 452 a . . . 452 n have the conventional two-part form: an if-partdefining a condition and a then-part defining a conclusion or actionthat is asserted if the condition is satisfied. Conditions can be simpleor they can be complex conjunctions or disjunctions of multipleassertions. An exemplary set of rules, which defines changes to be madeto the aligner, includes the following: if the motion of the tooth istoo fast, add driving material to the aligner opposite the desireddirection of motion; if the motion of the tooth is too slow, add drivingmaterial to overcorrect the position of the tooth; if the tooth is toofar short of the desired end position, add material to overcorrect; ifthe tooth has been moved too far past the desired end position, addmaterial to stiffen the aligner where the tooth moves to meet it; if amaximum amount of driving material has been added, add material toovercorrect the repositioning of the tooth and do not add drivingmaterial; if the motion of the tooth is in a direction other than thedesired direction, remove and add material so as to redirect the tooth.

In an alternative embodiment, illustrated in FIGS. 5B and 5C, anabsolute configuration of the aligner is computed, rather than anincremental difference. As shown in FIG. 5B, a process 460 computes anabsolute configuration for an aligner in a region of a current tooth.Using input data that has already been described, the process computesthe difference between the desired end position and the achieved endposition of the current tooth (462). Using the intersection of the toothcenter line with the level of the gum tissue as the point of reference,the process computes the complement of the difference in all six degreesof freedom of motion, namely three degrees of translation and threedegrees of rotation (step 464). Next, the model tooth is displaced fromits desired end position by the amounts of the complement differences(step 466), which is illustrated in FIG. 5B.

FIG. 5D shows a planar view of an illustrative model aligner 60 over anillustrative model tooth 62. The tooth is in its desired end positionand the aligner shape is defined by the tooth in this end position. Theactual motion of the tooth calculated by the finite element analysis isillustrated as placing the tooth in position 64 rather than in thedesired position 62. A complement of the computed end position isillustrated as position 66. The next step of process 460 (FIG. 5B)defines the aligner in the region of the current tooth in this iterationof the process by the position of the displaced model tooth (step 468)calculated in the preceding step (466). This computed alignerconfiguration in the region of the current tooth is illustrated in FIG.5D as shape 68 which is defined by the repositioned model tooth inposition 66.

A further step in process 460, which can also be implemented as a rule452 (FIG. 5A), is shown in FIG. 5C. To move the current tooth in thedirection of its central axis, the size of the model tooth defining thatregion of the aligner, or the amount of room allowed in the aligner forthe tooth, is made smaller in the area away from which the process hasdecided to move the tooth (step 465).

As shown in FIG. 6, the process 200 (FIG. 2B) of computing the shape foran aligner for a step in a treatment path is one step in a process 600of computing the shapes of a series of aligners. This process 600 beginswith an initialization step 602 in which initial data, control andconstraint values are obtained.

When an aligner configuration has been found for each step or segment ofthe treatment path (step 604), the process 600 determines whether all ofthe aligners are acceptable (step 606). If they are, the process iscomplete. Otherwise, the process optionally undertakes a set of steps610 in an attempt to calculate a set of acceptable aligners. First, oneor more of the constraints on the aligners is relaxed (step 612). Then,for each path segment with an unacceptable aligner, the process 200(FIG. 2B) of shaping an aligner is performed with the new constraints(step 614). If all the aligners are now acceptable, the process 600exits (step 616).

Aligners may be unacceptable for a variety of reasons, some of which arehandled by the process. For example, if any impossible movements wererequired (decision step 620), that is, if the shape calculation process200 (FIG. 2B) was required to effect a motion for which no rule oradjustment was available, the process 600 proceeds to execute a modulethat calculates the configuration of a hardware attachment to thesubject tooth to which forces can be applied to effect the requiredmotion (step 640). Because adding hardware can have an effect that ismore than local, when hardware is added to the model, the outer loop ofthe process 600 is executed again (step 642).

If no impossible movements were required (“no” branch from step 620),the process transfers control to a path definition process (such as step150, FIG. 2A) to redefine those parts of the treatment path havingunacceptable aligners (step 630). This step can include both changingthe increments of tooth motion, i.e., changing the segmentation, on thetreatment path, changing the path followed by one or more teeth in thetreatment path, or both. After the treatment path has been redefined,the outer loop of the process is executed again (step 632). Therecalculation is advantageously limited to recalculating only thosealigners on the redefined portions of the treatment path. If all thealigners are now acceptable, the process exits (step 634). Ifunacceptable aligners still remain, the process can be repeated until anacceptable set of aligners is found or an iteration limit is exceeded(step 650). At this point, as well as at other points in the processesthat are described in this specification, such as at the computation ofadditional hardware (step 640), the process can interact with a humanoperator, such as a clinician or technician, to request assistance (step652). Assistance that an operator provides can include defining orselecting suitable attachments to be attached to a tooth or a bone,defining an added elastic element to provide a needed force for one ormore segments of the treatment path, suggesting an alteration to thetreatment path, either in the motion path of a tooth or in thesegmentation of the treatment path, and approving a deviation from orrelaxation of an operative constraint.

As was mentioned above, the process 600 is defined and parameterized byvarious items of input data (step 602). In one implementation, thisinitializing and defining data includes the following items: aniteration limit for the outer loop of the overall process; specificationof figures of merit that are calculated to determine whether an aligneris good enough (see FIG. 2B, step 270); a specification of the alignermaterial; a specification of the constraints that the shape orconfiguration of an aligner must satisfy to be acceptable; aspecification of the forces and positioning motions and velocities thatare orthodontically acceptable; an initial treatment path, whichincludes the motion path for each tooth and a segmentation of thetreatment path into segments, each segment to be accomplished by onealigner; a specification of the shapes and positions of any anchorsinstalled on the teeth or otherwise; and a specification of a model forthe jaw bone and other tissues in or on which the teeth are situated (inthe implementation being described, this model consists of a model of aviscous substrate fluid in which the teeth are embedded and which hasboundary conditions that essentially define a container for the fluid).

FIG. 7 is an exemplary diagram of a statistical root model. As showntherein, using the scanning processes described above, a scanned upperportion 701 of a tooth is identified. The scanned upper portion,including the crown, is then supplemented with a modeled 3D root. The 3Dmodel of the root can be statistically modeled. The 3D model of the root702 and the 3D model of the upper portion 700 together form a complete3D model of a tooth.

FIG. 8 shows exemplary diagrams of root modeling, as enhanced usingadditional dental information. In FIG. 8, the additional dentalinformation is X-ray information. An X-ray image 710 of teeth is scannedto provide a 2D view of the complete tooth shapes. An outline of atarget tooth is identified in the X-Ray image. The model 712 asdeveloped in FIG. 7 is modified in accordance with the additionalinformation. In one embodiment, the tooth model of FIG. 7 is morphed toform a new model 714 that conforms with the X-ray data.

FIG. 9 shows an exemplary diagram of a CT scan of teeth. In thisembodiment, the roots are derived directly from a high-resolution CBCTscan of the patient. Scanned roots can then be applied to crowns derivedfrom an impression, or used with the existing crowns extracted from ConeBeam Computed Tomography (CBCT) data. A CBCT single scan gives 3D dataand multiple forms of X-ray-like data. PVS impressions are avoided.

In one embodiment, a cone beam x-ray source and a 2D area detector scansthe patient's dental anatomy, preferably over a 360 degree angular rangeand along its entire length, by any one of various methods wherein theposition of the area detector is fixed relative to the source, andrelative rotational and translational movement between the source andobject provides the scanning (irradiation of the object by radiationenergy). As a result of the relative movement of the cone beam source toa plurality of source positions (i.e., “views”) along the scan path, thedetector acquires a corresponding plurality of sequential sets of conebeam projection data (also referred to herein as cone beam data orprojection data), each set of cone beam data being representative ofx-ray attenuation caused by the object at a respective one of the sourcepositions.

FIG. 10 shows an exemplary user interface showing the erupted teeth,which can be shown with root information in another embodiment. Eachtooth is individually adjustable using a suitable handle. In theembodiment of FIG. 10, the handle allows an operator to move the toothin three-dimensions with six degrees of freedom.

The teeth movement is guided in part using a root-based sequencingsystem. In one embodiment, the movement is constrained by a surface areaconstraint, while in another embodiment, the movement is constrained bya volume constraint.

In one embodiment, the system determines a surface area for each toothmodel. The system then sums all surface areas for all tooth models to bemoved. Next, the system sums all surface areas of all tooth models onthe arch. For each stage of teeth movement, the system checks that apredetermined area ratio or constraint is met while the tooth models aremoved. In one implementation, the constraint can be to ensure that thesurface areas of moving teeth are less than the total surface areas ofteeth on an arch supporting the teeth being moved. If the ratio isgreater than a particular number such as 50%, the system indicates anerror signal to an operator to indicate that the teeth should be movedon a slower basis.

In another embodiment, the system determines the volume for each toothmodel. The system then sums the volumes for all tooth models beingmoved. Next, the system determines the total volume of all tooth modelson the arch. For each stage of teeth movement, the system checks that apredetermined volume ratio or constraint is met while the tooth modelsare moved. In one implementation, the constraint can be to ensure thatthe volume for moving teeth is less than the volume of all teeth on anarch supporting the teeth being moved. If the ratio is greater than aparticular number such as 50%, the system indicates an error signal toan operator to indicate that the teeth should be moved on a slowerbasis.

Optionally, other features are added to the tooth model data sets toproduce desired features in the aligners. For example, it may bedesirable to add digital wax patches to define cavities or recesses tomaintain a space between the aligner and particular regions of the teethor jaw. It may also be desirable to add digital wax patches to definecorrugated or other structural forms to create regions having particularstiffness or other structural properties. In manufacturing processesthat rely on generation of positive models to produce the repositioningappliance, adding a wax patch to the digital model will generate apositive mold that has the same added wax patch geometry. This can bedone globally in defining the base shape of the aligners or in thecalculation of particular aligner shapes. One feature that can be addedis a rim around the gumline, which can be produced by adding a digitalmodel wire at the gumline of the digital model teeth from which thealigner is manufactured. When an aligner is manufactured by pressurefitting polymeric material over a positive physical model of the digitalteeth, the wire along the gumlines causes the aligner to have a rimaround it providing additional stiffness along the gumline.

In another optional manufacturing technique, two or more sheets ofmaterial are pressure fit over the positive tooth model, where one ofthe sheets is cut along the apex arch of the aligner and the other(s) isoverlaid on top. This provides at least a double thickness of alignermaterial along the vertical walls of the teeth.

The changes that can be made to the design of an aligner are constrainedby the manufacturing technique that will be used to produce it. Forexample, if the aligner will be made by pressure fitting a polymericsheet over a positive model, the thickness of the aligner is determinedby the thickness of the sheet. As a consequence, the system willgenerally adjust the performance of the aligner by changing theorientation of the model teeth, the sizes of parts of the model teeth,the position and selection of attachments, and the addition or removalof material (e.g., adding virtual wires or creating dimples) to changethe structure of the aligner. The system can optionally adjust thealigner by specifying that one or more of the aligners are to be made ofa sheet of a thickness other than the standard one, to provide more orless force to the teeth. On the other hand, if the aligner will be madeby a rapid prototyping process (e.g., stereo or photo lithographyprocess), the thickness of the aligner can be varied locally, andstructural features such as rims, dimples, and corrugations can be addedwithout modifying the digital model of the teeth.

The system can also be used to model the effects of more traditionalappliances such as retainers and braces and therefore be used togenerate optimal designs and treatment programs for particular patients.

FIGS. 11A-11B illustrate an initial tooth position with a positioneddental appliance, and a resulting undesirable force vector,respectively. Referring to the Figures, in an example where the tooth asshown is being moved in a facial direction along the x-direction, uponpositioning of the dental appliance such as the polymeric shell aligner,over the tooth, the aligner shape geometry is configured to apply apredetermined force upon the tooth to reposition the tooth in accordancewith a treatment plan for the particular treatment stage. For example,as shown in FIG. 11B, the dental appliance is configured to engage thetooth to reposition the tooth in the x-direction as shown, but, rather,results in the application of a predetermined force in the +x/−zdirection as shown and illustrated by the arrow.

Accordingly, in one aspect, the aligner shape geometry may be optimizedto compensate for the undesirable but resulting force vector so as tocounteract its force and further, to apply the intended force in thedirection based on the treatment plan for the treatment stage underconsideration. That is, FIGS. 11C-11D illustrate a relief addition tothe dental appliance to counteract the undesirable force vector aroundthe tooth, and the resulting desired application of the predeterminedforce on the tooth by the dental appliance, respectively. In one aspect,to compensate for the undesirable force (for example, as shown in FIG.11B by the arrow), a predetermined relief (for example, but not limitedto, 0.1 to 0.3 mm) may be provided such that the contact between thealigner and the tooth that resulted in the undesirable force vector isavoided, but still retaining the desired force, for example, along thex-axis as discussed above.

Referring to FIGS. 11C, the predetermined relief on the aligner isillustrated by the shown arrow, whereby the engagement between thealigner and the tooth at the location resulting in the undesirable forceis removed by modifying the shape of the aligner geometry. In thismanner, in one aspect, and as shown in FIG. 11D, the intended anddesirable force applied upon the tooth for example, in the x-direction,is achieved by, for example, modifying the aligner shape geometry.

FIG. 12 illustrates a modified dental appliance geometry including anadditional shape modification to remove a gap between the dentalappliance and the tooth. Referring to FIG. 12, it is to be noted thatwhile the modification of the aligner shape geometry (for example,discussed above in conjunction with FIGS. 11C-11D), results in thedesired predetermined force applied upon the tooth as planned for thedental treatment, there may be a gap or pocket that forms between thetooth and the aligner, for example, as shown in FIG. 12, near thegingival area. In one aspect, to account for this gap or pocketgenerated, the aligner shape geometry may be further modified oroptimized, for example, to better adapt in the direction towards thetooth when the aligner is in the active (or stretched) state.

Referring to FIG. 12, the optimization of the aligner shape geometry toaddress the formed gap or pocket is illustrated by the arrow in oneembodiment, in the direction of which, the aligner shape may bemodified. Moreover, it should be noted that the optimization of thealigner shape to account for the gap may potentially effect thedirection of the applied force on the tooth by the aligner, and thus,may further require additional modification or optimization.

In one aspect, the modification of the dental aligner shape geometrywith one or more areas of relief, as well as recontouring for looser ortighter adaptation, respectively, to achieve the desired force vector,while avoiding friction and other undesirable force vectors providesimproved and customized aligner shape for the treatment of the dentalconditions.

In manufacturing of the dental appliances, in one aspect, the moldformed by rapid prototyping may be adjusted during the build process totake shape of the desired geometry based on, for example, digitallyadding and/or subtracting the relief and/or protrusion in predefined orrelevant locations of the mold.

FIG. 13 illustrates dental appliance shape geometry configuration basedon sweep geometry of the treatment plan for a tooth. Referring to FIG.13, in one aspect, since friction between the dental aligner and thetooth may impose limitations to the treatment, in one aspect, thealigner shape geometry may be optimized by removing all interferencesbetween the current position (at the current treatment stage), and thenext position (the n+1 treatment stage). That is, a sweep geometrybetween the current position and the next position may be generated. Thesweep geometry as illustrated in FIG. 13 is the union geometry betweenthe current position and the next infinitely small increment towards thenext position (n+1 treatment stage). By adding up the infinitely smallincrements, the resulting geometry establishes the sweep geometry shape.

Referring again to FIG. 13, after determining the sweep geometry for thealigner to minimize or remove friction between the tooth and the dentalaligner, one or more distortions or relief may be added to the alignershape to provide the desired movement vector to apply the intended forcein the direction as determined for the particular treatment stage forthe treatment plan.

In a further aspect, it is possible to detect when a tooth movement willbe less likely as a result of inadequate force generation. That is, theamount of surface area perpendicular to the desired line of movement (orto the direction of the movement vector) may be insufficient for thealigner to deliver the necessary force. For example, in the extrusivedirection (along the+Z axis, as shown in FIG. 12), there may beinsufficient undercut present to enable a tooth to be pushed along thisdirection. As a result, a dental attachment may be added or provided onthe tooth to improve the amount of surface area perpendicular to thedesired direction of tooth movement.

In one aspect, based on the force behavior determined from the materialproperties and the amount of surface area perpendicular to the compositevector resulting from the movement vector for the particular treatmentstage, additional surface area may be added to the tooth by employing adental attachment specifically suited for the desired movement. In thismanner, in one aspect, the cross section of the surface area may bedetermined for a particular tooth, and the dental attachment may bepositioned thereon, to enhance or improve upon the necessary surfacearea to cooperate or engage with the dental appliance to effect thedesired movement vector or the predetermined level of force upon thetooth in the accurate direction for the treatment stage.

In this manner, in one aspect, a dental aligner may be manufactured orsimulated using a computer aided design tool or system, where, arepresentation of the tooth to be moved is first modeled. Thereafter,the aligner that defines the target position of the tooth is modeledwith shape geometry properties defined. Thereafter, the force necessaryto reposition the tooth from the initial location to the target locationis determined or modeled, for example, using FEA modeling or othersuitable computation and/or modeling techniques. In one aspect, it ispossible to define the force using a physical model of the teethconnected to force measurement sensors, such that the optimal forces maybe determined using the readouts obtained from the physical model, andthus altering the shapes of attachments and aligner configurations basedat least in part on the feedback from the physical force gauge.

As a result, a movement vector is defined which establishes thedirection of the applied force, as well as the level of force and itsproperties which are necessary to reposition the tooth from the initialposition to the target position. Based on the movement vector, and themodeled aligner shape, the aligner is further modified or reconfiguredto factor in the determined movement vector. That is, after havingdefined the movement vector which identifies the force propertiesnecessary for the tooth repositioning, the dental appliance shape isaltered or optimized based on the determined movement vector.Additionally, the appliance shape may be further optimized to counteractthe undesirable forces or force components that may result based on thedefined movement vector.

Thereafter, the modified or optimized dental appliance may bemanufactured through rapid prototyping or other suitable techniques toattain the desired tooth movement. Further, this process may be repeatedfor the optimization of dental appliance for each treatment stage of thetreatment plan such that the aligner performance and therefore, thetreatment plan result is improved.

Additionally, in one aspect, there is provided an interactive analysisprocess where minute or small localized changes are introduced into thealigner shape geometry, and wherein the effect of the resulting forceprofile is compared to the desired force, for example, in each treatmentstage of a treatment plan, and repeated if the result is closer to thetarget profile, and ignored if the results move away or deviate furtherfrom the target profile. This may be repeated for each treatment stageof the treatment plan such that the series of dental appliances oraligners are each optimized in its respective shape geometry to improvetreatment results.

In a further aspect, in one embodiment, the dental applianceconfiguration may be based on sweep geometry discussed above to minimizefriction between the dental appliance and the respective tooth, andfurther, the dental appliance may be modified to create one or moreindividual contact points or surfaces (for example, dimples or contactsusing attachments bonded to teeth) to generate the desired force. Theresulting dental appliance geometry including the current and thesubsequent (n+1 stage) sweep path geometry as well as the forcegenerating movements such as the movement vector discussed above, may bemodeled using for example, a computer aided design or modeling tool.

Furthermore, in yet still another aspect, dental attachment placementmay be determined based on the location of the maximum amount of surfacearea available perpendicular to the desired direction of the toothmovement. Further, if the force on any given tooth in the treatment planis at or below a predefined level, the attachment may be added to thetooth to supplement the desired surface area or increase the frictioncoefficient of the tooth thereby improving the force profile of thealigner of the tooth.

In one aspect, the data set associated with the teeth, gingiva and/orother oral tissue or structures may be intentionally altered through,for example, addition, partial or total subtraction, uniform ornon-uniform scaling, Boolean or non-Boolean algorithm, or geometricoperations, or one or more combinations thereof, for the configuration,modeling and/or manufacturing of the dental appliance that may beoptimized for the desired or intended treatment goal.

Moreover, referring to the discussion above regarding attachments,angulation or the attachment as well as the surface configuration of theattachments may be provided to improve upon the movement vector tooptimize its application to the desired tooth while minimizing theamount of undesirable or unwanted force vectors that may becounteracting upon the movement vector. Additionally, in one aspect, aseries of abutting attachments may be provided to alter the forcedirection or generate the movement vector which is carried over for apredetermined time period, such that, the series of abutting attachmentsmay be configured to function as a slow motion cams where the dentalappliance then functions as a follower.

In still another aspect, point tracing may be added to treat and/ortrack tooth points over the treatment stages, such that the desired orproper cam/follower relationship may be determined to attain the targetposition or the treatment goal. In one aspect, one or more protrusionson the interior surface(s) of the dental appliance may be configured asthe follower, and which may be formed from virtual pressure points. Thevirtual pressure points are comprised in one embodiment of voidsintentionally build or designed into the reference mold or model, whichis associated with corresponding portions in the aligner that areindented to exert additional pressure on the teeth when the aligner isformed over the reference mold.

FIGS. 14A-14B illustrate dental attachment positioning for toothrotation. Referring to FIGS. 14A-14B, a pair of attachments arepositioned on buccal and lingual surfaces of a tooth as shown, with thecenters positioned in a plane that is perpendicular to the Z-axisrelative to the tooth. Referring to the Figures, the two attachments aredisplaced or biased in opposite directions as shown by the respectivearrows in the figures, in the aforementioned plane, to generate acouple, which corresponds to a torque with a zero net force, resultingin a rotational movement of the tooth.

FIG. 15 illustrates dental attachment positioning for tooth inclination.Referring to FIG. 15, one attachment may be positioned on buccal surfacewhile another attachment is positioned on the lingual surface with adifference in their relative height with the center or axis positionedin a plane perpendicular to the Y-axis of relative to the tooth. Forceis applied on the attachments in the direction as shown by the arrows,resulting in a torque along the Y-axis relative to the tooth position,and with the resulting net force being zero. In another aspect, theattachments may be positioned in a plane perpendicular to the Y-axisrelative to the tooth. In this manner, the application of force on theattachments to translate one attachment towards the occlusal and theother in the opposite direction in the same plane results in aninclination of the tooth. This approach may be used, for example, inorthodontic root torquing (lingual root inclination), where the centerof rotation for the tooth is in the crown and thus the root will betipped or inclined.

FIG. 16 illustrates dental attachment positioning for tooth angulation.As shown, the pair of attachments are positioned on the tooth withrespective forces applied thereon as shown by the respective arrows.This effect results in the angulation of the tooth (for example, in theclockwise direction in the embodiment shown in FIG. 16).

FIGS. 17A-17B illustrate dental attachment positioning for buccaltranslation and lingual translation, respectively. Referring to theFigures, the pair of attachments as shown may be positioned on both thebuccal and lingual sides in an X-Y plane relative to the tooth. With twoattachments positioned at different heights to the center of rotation ofthe tooth, the attachment that is positioned closer to the center ofrotation is pushed into the tooth crown more than the attachment that isrelatively further away from the center of rotation. Therefore, thetotal force on the tooth will be a positive value, but the tippingtorque may be adjusted to zero, since the force lever component to thecenter of rotation from each of the two attachments may be adjustedequally opposite to each other. This approach allows for the tooth roottranslation.

FIGS. 18A-18B illustrate dental attachment positioning for mesial anddistal translation, respectively. Referring to the Figures, mesial anddistal translation of the tooth may be obtained, for example, by thepositioning of the pair of attachments as shown in the Figures, with thesuitable predetermined force applied thereon.

FIGS. 19A-19B illustrate dental attachment positioning for extrusion andintrusion, respectively. Referring to the Figures, the pair ofattachments in this case are positioned on the lingual and buccal sidesof the tooth, with the centers in the plane that also includes the Zaxis. Both attachments as shown are configured to move up along theZ-axis for extrusion or move down along the Z-axis for intrusion. Theforce generated or applied upon the two attachments are different inmagnitude (for example, resulting from different local attachmentmovement with respect to the tooth crown). When the force from theattachments result in force-lever to the center of rotation that areequally opposite, the tipping torque may be cancelled out, and theresulting force may include extrusion or intrusion translation of thetooth.

Furthermore the attachment movement resulting in the extrusion orintrusion translation described above may be used with the translationmovement on tooth crown to obtain counter balance torque. For example,the tipping torque resulting from the buccal movement may be counterbalanced by configuring an attachment to move relative to the crown tothe occlusal plane on the buccal surface.

Additionally, the attachment movement resulting in the extrusion orintrusion translation may be used with locally inflated aligners thatinclude aligner surfaces which are ballooned on some tooth crowns suchthat the aligner surface does not contact the tooth crowns in a passivestate. When an inflated aligner is used with attachment movement forrotation, the maximum rotation torque and minimum unwanted force may beobtained, because the aligner only interferes with attachments togenerate a rotation couple with zero total force, for example.

In still a further embodiment, pre-fabricated attachments may be used toreduce or eliminate failure due to incorrect attachment shape forming.

Accordingly, in one aspect, the n+1 or subsequent/target tooth positionis first determined. Thereafter, the direction of movement to reach thetarget tooth position from the initial tooth position is determined.After determining the direction of movement, the amount or magnitude anddirection of force and torque to reposition the tooth from the initialposition to the target position is determined. Thereafter, profile ofthe attachment such as the geometry that would provide the most suitablegrip in the direction of the planned tooth movement is determined, aswell as the optimal position of the attachment relative to the toothsurface.

Having determined the relevant profile of the attachments, theattachment displacement to attain the position translation from theinitial position to the target position is determined. Upon positioningthe attachment on the tooth, the dental appliance at the subsequenttreatment stage engages with and contacts the dental appliance via thepositioned attachment.

In this manner, the force/torque generated by the dental appliance isaccurately directed in the desired direction, and also is configuredwith sufficient magnitude to move the tooth into the next plannedposition. For example, in one embodiment, the attachments are bonded tothe patient's tooth. The initial position of the attachment isdetermined as described above. The displaced or repositioned attachmentsmay generate a new position of the cavities conforming to the shape ofthe attachment on the dental appliance. With the attachments on toothcrown at the initial stage and displaced at the subsequent targettreatment stage, the dental appliance of the target treatment stage mayinterfere with the attachment on the tooth at the initial treatmentstage. The interference in turn, is configured to generate theforce/torque to create the desired tooth movement.

In one aspect, the direction and the magnitude of the force/torque maybe modified or optimized to generate counter-balancing force/torque toeliminate or minimize unwanted tipping torque, to attain root movement,and the like, by adjusting the amount of the attachment displacementrelative to the crown surface, for example. The amount of the attachmentmovement with respect to the tooth crown may also be correlated with thetooth movement to generate a treatment plan based on the movement of theattachment.

FIG. 20 illustrates a complementary engagement of the dental applianceand the attachment. Referring to FIG. 20, in one aspect, a protrusion ora button is provided on the dental appliance such as that shown in FIG.20 (labeled (a)) which in one embodiment is configured to engage with acorresponding groove or dimple on the attachment (labeled (b)) shown inFIG. 20 and which is positioned on the tooth surface. In this manner,with the button or protrusion on the dental appliance and the cavity onthe attachment to receive the protrusion, the relative position of theprotrusion may be configured to apply a point or surface area force onthe attachment device.

Accordingly, the protrusion on the dental appliance or aligner and thecavity on the receiving attachment device may be configured to form ajoint or engagement where point force may be exerted. Furthermore, inthe event that the relative position of the protrusion on the dentalappliance and the cavity on the attachment is modified locally (forexample, based on one or more movement translations discussed above),the point or surface area force may be oriented to cause correspondingtooth movement.

Moreover, in one aspect of the present disclosure, the surface areawhich is configured to provide the altered tooth facing point force mayinclude a ridge or a flat protrusion inwards towards the tooth.Additionally, the force may also include a “reinforced” surface area atthe n+1 stage, where, in one aspect, corrugation may be implemented byone or more ridges or folds, such that the inner surface facing thetooth remains in full contact (rather than to point or ridge) with thetooth and is reinforced in the localized supported area such that theforce does not dissipate as easily as in areas where they areunsupported.

FIG. 21 is a flowchart illustrating the optimized shape geometry of thedental appliance. Referring to FIG. 21, at step 2110, the initialposition of the tooth is determined. Thereafter, at step 2120, thetarget position of the tooth based on the treatment plan is determined.In one aspect, the target position may include the next or n+1 treatmentstage tooth position. Referring back to FIG. 21, after determining thetarget position of the tooth based on the treatment plan, a movementvector associated with the tooth movement from the initial position tothe target position is calculated or determined at step 2130. That is, aforce profile or attribute is determined which includes, for example,the magnitude of the force and the direction of the force, for example,that is associated with the tooth movement from the initial position tothe target position.

Referring again to FIG. 21, after determining the movement vectorassociated with the tooth movement from the initial position to thetarget position, at step 2140, the components associated with themovement vector are determined. For example, as discussed above, theforce magnitude associated with the movement vector to reposition thetooth from the initial position to the target position is determined.Additionally, the force direction for the tooth movement, as well ascounter forces for addressing unwanted or unintended forces aredetermined. Thereafter, based on the determined components associatedwith the movement vector which is associated with the tooth movementfrom the initial position to the target position, the cavity geometry ofthe dental appliance such as the aligner is modified.

FIG. 22 is a flowchart illustrating the dental attachment positioning.Referring to FIG. 22, at step 2210 the tooth position at a firsttreatment stage is determined. At step 2220 the tooth position at thesecond or n+1 treatment stage is determined. Thereafter, the movementvector associated with the tooth movement from the first treatment stageto the second treatment stage is determined at step 2230. Afterdetermining the movement vector associated with the tooth movement, oneor more dental attachment profiles associated with the movement vectoris determined at step 2240. That is, the position of the dentalattachment, the angulation of the dental attachment, the surface areaperpendicular to the direction of the force from the dental appliance,for example, are determined. Thereafter, at step 2250, the one or moredental attachments are positioned on the corresponding tooth during thefirst treatment stage.

In this manner, in one embodiment, the force/torque from the dentalappliance is accurately applied to the tooth to reposition the toothfrom the initial position to the target or second treatment stageposition.

Referring to FIG. 23, at step 2310, for a stage in the sequence of stepsto move teeth from an initial position to a targeted final position,trajectories of every point on each tooth's surface are computed for agiven predetermined stage movement. From the trajectories, activesurfaces of the teeth are determined 2320. The active surfaces arecalculated to be all the points p on tooth surfaces such that theprojection of the normal force N(p) to the surface of the tooth at pointp onto the tangent vector of the trajectory Γ_(p) corresponding to thedesired movement, is greater than a predefined positive threshold. Oncethe active surfaces are determined, a ratio between the active surfacesand the resistance surface of the roots of the teeth is calculated 2330for each tooth of the patient. If this ratio is greater than apredefined threshold, then the tooth has adequate active tooth surfacesfor the required tooth movement 2340.

Still referring to FIG. 23, if the ratio between the active surfaces andthe resistance surfaces of the roots of the teeth is not greater than apredefined threshold, then minimal variation of the existing toothsurface may be done 2350. Variations to the existing tooth surface mayinclude, among others, a custom attachment or appliance to increase thenumber of active surfaces of the tooth or addition of a material to thesurface of the tooth. The minimal variations of the existing toothsurface should satisfy the following constraints; the modified surfaceprovides active surfaces for the required movement with the ratiogreater than the threshold between the active surfaces and resistancesurfaces, the modified surface is a variation of an accessible surfaceof the tooth in its current position, and the modified surface mustsatisfy requirements of manufacturability. Once the existing toothsurface is modified, the new surface is verified with the correspondingaligner to assure that enough contact area with the modified toothsurface exists by repeating steps 2310-2330 for the modified toothsurface.

FIG. 24 is a flowchart illustrating a method of determining whether anattachment is desirable to obtain sufficient active surface area of atooth. Referring to FIG. 24, at step 2410, for a given treatment stagein the sequence of stages for a treatment plan to move teeth from aninitial position to a target position, a rigid body transform A for atooth may be determined. In one aspect, the rigid body transform A mayinclude a rigid body transformation moving tooth from a position atstage n to a position at stage n+1.

Referring to FIG. 24, from the rigid body transform A, a geodesic curveA(t) in the space of rigid body transforms correlating the rigid bodytransformation corresponding to zero movement I and the rigid bodytransform A is determined (2420). For example, in one aspect, the rigidbody transform corresponding to zero movement I correlates to where allpoints remain the same without movement or displacement. For each vertexV on the surface of the tooth, a dot product s(V) of the unit tangentvector to the curve A(t)V at t=0 with inner normal unit vector N to thetooth's surface at V is computed 2430.

Thereafter, the active surfaces of the tooth as the set of all faces ofthe crown having at least one vertex V where s(V) is greater than apredefined threshold SC is determined (2440). That is, in one aspect,when the angle between the direction of the crown point movement and thesurface inner normal at this point is larger than the predefinedthreshold SC, the crown point may be considered to be active crownsurface. Referring again to FIG. 24, the resistance surface of the toothas the set of all faces of the root having at least one vertex V, wheres(V) is smaller than a predefined threshold SR is determined (2450). Ina further aspect, if the angle between the direction of root pointmovement and surface inner normal at this point is larger than thepredefined threshold SR, then the root point may be considered to be onthe resistance root surface.

Referring still again to FIG. 24, the ratio G may be determined as theratio of the areas of the active surfaces and resistances surfaces(2460). If the ratio G is greater than the predefinedactive-to-resistance threshold AR, then no attachment may be needed(2470). For example, in one aspect, if the ratio of area of the crownactive surface to the area of root resistance surface is greater thanthe predefined active-to-resistance threshold AR, the movement may beconsidered feasible. On the other hand, if the ratio G is not greaterthan AR, then a minimal addition to the crown surface, such thatrecomputed ratio G satisfies the condition of G>AR is used (2480). Thisaddition may be made as an attachment, such as a ridge, protrusion, ordimple, among others, and may be engaged to the crown of the tooth.

According to an embodiment, a non-iterative process is used fordetermining a near-optimal shape of the aligner for the desired movementaccording to a treatment plan. FIG. 25 is a flowchart of thisnon-iterative process 800. For an elementary shape feature (e.g., adimple), the magnitude of the force developed by the feature is computedas a function of the position of the feature on the surface of thealigner and of the feature prominence at step 810. This function may bederived statistically by relating the geometric characteristic of afeature location (e.g., distance to the boundary, distance to theinflection ridge, curvature, etc.) with the value of the magnitude offorce generated by the feature. For a given movement of a tooth fromstage n to stage n+1, the rotation axis through the center of resistanceand translation vector corresponding to the given movement is computedat step 820. Next, at step 830, points on the tooth surface areidentified where the forces would be applied, and the magnitude offorces are computed such that, if the forces with these magnitudes areapplied at the identified points in the direction of their trajectoriesof movement from stage n to stage n+1, then the following conditions aremet:

-   -   a. total torque axis through the center of resistance would be        close to the required rotation axis direction    -   b. total torque magnitude would be sufficient for the tooth        rotation    -   c. total force direction would be close to direction of        translation vector    -   d. total force magnitude would be sufficient for translation of        the tooth.

Among the sets of points satisfying the above conditions, the sets ofpoints satisfying the following constraints is then identified at step840:

-   -   a. Number of points is the least possible    -   b. Points are as far apart as possible    -   c. Points as close as possible to the active surface of the        tooth.

For the point sets identified in step 840, the surface of theattachments required (if any) to convert the point location into activesurface for the required tooth movement is computed at step 850. Then,the point set with no more than one attachment, which is on buccal sideof the tooth, with conditions of the step 830 satisfied as close aspossible, is chosen at step 860. Then, at step 870, the shape features(e.g., dimples) are created at the identified point set with prominencecorresponding to the desired force magnitudes. At optional step 880, ifpoints are located close to each other, the corresponding dimples can bemerged to form ridges. The skilled artisan will appreciate that theresulting dimples and ridges are the aligner shape features required forthe desired movement of the tooth.

FIG. 26 shows the trajectories of crown points from a first treatmentstage to a second treatment stage of a treatment plan in one aspect.Referring to FIG. 26, the crown of a tooth 2501 has points 2511 and 2521in an initial position of a treatment stage of the treatment plan. At adesired treatment stage of the treatment plan, the equivalent points ofthe crown of a tooth 2501 may be displaced to target locations 2512 and2522. The trajectories 2513 and 2523 may be determined and mapped basedon the initial and target position of the crown of the tooth.

FIG. 27 shows the active surface and resistance surface of a tooth inone aspect. Referring to FIG. 27, the crown of a tooth 2501, has activesurfaces 2530, or surfaces onto which force may be applied to move atooth in a desired trajectory 2513 and 2523. Working against theseactive surfaces may include forces applied on resistance surfaces 2540located on the root of a tooth 2502. When the ratio of the activesurfaces to the resistance surfaces is greater than a predefinedthreshold, the correct forces may be applied, for example by shapedaligners, to move the tooth along the desired trajectory 2513 and 2523.

FIG. 28 demonstrates the increase in active surface of a tooth by theaddition of an attachment. Referring to FIG. 28, in the case where theratio of active surfaces to resistance surfaces is not initially greaterthan a predefined threshold, additions, such as attachments 2550including ridges, dimples, or protrusions, may be engaged to the toothin order to increase the active surfaces 2530 of a tooth. By increasingthe amount of active surfaces 2530 by the use of an attachment, theratio between the active and resistance surfaces may then be greaterthan the predefined threshold, thus allowing forces to be applied forthe correct movement of a tooth along a desired trajectory 2513.

FIG. 29 shows a cross-section of a tooth with an attachment and alignerwith a ridge to match the attachment. Referring to FIG. 29, in order toachieve a desired tooth movement, sometimes an attachment 2550 may beused to increase the active surface area of a tooth crown's surface2501. In order for the attachment to be effective, correct forces mustbe applied to the attachment 2550 in order to move the tooth along thedesired trajectory path. These forces are created by ridges 2561, or anyequivalent, in a shaped aligner 2560 that fit to the attachment 2550. Inthis way the aligner 2560 applies the correct forces directly to thetooth surface, as well as to the attachment 2550 in order to move thetooth along the desired trajectory from an initial position to a desiredtarget position.

In the manner described, in one aspect, an orthodontic treatment planmay be generated based at least in part, on the patient's initialdentition in its initial position, and the desired treatment outcomeincluding, for example, the location and orientation of the teeth at theend of the treatment. In one aspect, computer software implementedapproach may be used to analyze the path of each tooth from its initialto final position. All movements in three dimensional spaces may beanalyzed. For example, the path may be described as a series ofincremental movements, where each increment may include a combination oflinear displacements and rotations. The loadings—forces andmoments—required to accomplish the desired movement may be determinedbased, for example, at least in part on the loadings that may inducemovement through the next increment of movement on the path to the finaltarget position, or may induce one movement which encompasses the totalmovement from the initial location to the final target position.

In one aspect, the surface of the tooth may be analyzed and defined as acompilation of discrete smaller surfaces. The surfaces with orientationsdesirable to the required direction or the loading may be identified. Ifno such surface(s) exists or are not optimal for the required loadapplication, or cannot be accessed intraorally, the toothsurface/orientation may be contoured for improvement or altered byadding material. In this manner, in one aspect, the approach describedherein may determine one or more possible solutions to providecorrection to the force system desired, and determine one or moreclinically viable solutions.

In a further aspect, more than one force on more than one surface may berequired to impart the correct force system for the prescribed movement.It will be understood that the dental appliance is configured to apply aforce system on a tooth and that a force system comprises at least oneof a force, a moment of a force, and a moment of a couple. Accordingly,variations may be made to the aligner geometry such that the designatedforce system may be delivered on the surfaces as identified, forexample, by the one or more viable solutions determined. Variations inaligner geometric parameters may result in variations in the points ofcontact of the aligner and tooth, and control the force system appliedto the particular tooth. The variations may be calibrated to control theforce system and initiate tooth movement. Also, specific features suchas, but not limited to, ridges, may be included to attain control ofcontact points on the surfaces and provide the necessary loading.

In yet a further aspect, the aligner geometry may be provided with arelief area or bubble to allow unhindered movement of the tooth intothat area or location. The force system applied to the tooth by thealigner may move the tooth unchallenged within the open spaceencompassed by the aligner.

In still another aspect, the aligner features may be designed andfabricated to limit movement of the tooth. For example, the aligner maybe designed to be a physical boundary through which the tooth cannotmove providing safety against unwanted movements that may be deleteriousto the patient's health. Further, the aligner in another aspect may beconfigured to function as a guiding surface along which the tooth moves.More particularly, the aligner may be configured to impart a forcesystem to the tooth and the tooth may be guided into a specific locationand orientation assisted by the guidance of the aligner.

In this manner, incorporation of one or more features into an alignergeometry or configuration may result in a subsequent change of thegeometry of the aligner, the alterations resulting in changes in thelocation of the contact surfaces of the tooth and the aligner. Thechanges and the effects of these geometric changes may be determined andcompensated by identifying new surfaces and loadings to accomplish thedesired movement. The aligner geometry may be improved in such iterativedesign process as each iteration may be configured to consider eachfeature and its effect on the aligner geometry, on the surfaces ofcontact and on the force system produced, before defining the finalaligner design, and also, the overall treatment plan including thetreatment stages.

In the manner described, in one aspect, orthodontic treatment approachmay include defining the path of movement of each tooth, the forcesystem required to attain the movement, determination of the surfacesand the forces to be applied to those surfaces to impart the definedforce system, and the geometric designs of aligners that satisfies suchtreatment criteria.

A computer implemented method in one embodiment includes establishing aninitial position of a tooth, determining a target position of the toothin a treatment plan, calculating a movement vector associated with thetooth movement from the initial position to the target position,determining a plurality of components corresponding to the movementvector, and determining a corresponding one or more positions of arespective one or more attachment devices relative to a surface plane ofthe tooth such that the one or more attachment devices engages with adental appliance.

The one or more attachment devices may be configured to apply apredetermined force on the dental appliance substantially at the surfaceplane of the tooth.

In one aspect, the plurality of components may provide one or more of arotational displacement of the tooth, an angular displacement of thetooth, a linear displacement of the tooth, or one or more combinationsthereof.

The dental appliance may include a polymeric shell.

Further, one or more of the plurality of components may correspond to arespective one or more force or moment of force applied by the dentalappliance on the respective attachment device, where the one or more ofthe plurality of components may correspond to a respective one or moreforce or moment of force applied by the respective attachment device onthe dental appliance.

The one or more attachment devices may include a plurality of dentalattachment devices provided on the tooth in an abutting positionrelative to each other, where the dental appliance may be configured tophysically contact each of the plurality of the abutting dentalattachment devices sequentially, and separately for a predeterminedperiod of time.

An apparatus for modeling a dental appliance in another embodimentincludes a data storage unit, and a processing unit coupled to the datastorage unit and configured to determine an initial position of a tooth,determine a target position of the tooth in a treatment plan, calculatea movement vector associated with the tooth movement from the initialposition to the target position, determine a plurality of componentscorresponding to the movement vector, and determine a corresponding oneor more positions of a respective one or more attachment devicesrelative to a surface plane of the tooth such that the one or moreattachment devices engages with a dental appliance.

In one aspect, the one or more attachment devices may be configured toapply a predetermined force on the dental appliance substantially at thesurface plane of the tooth.

Further, the plurality of components may provide one or more of arotational displacement of the tooth, an angular displacement of thetooth, a linear displacement of the tooth, or one or more combinationsthereof.

Moreover, the dental appliance may include a polymeric shell.

The one or more of the plurality of components may include a respectiveone or more force or moment of force applied by the dental appliance onthe respective attachment device, where the one or more of the pluralityof components may correspond to a respective one or more force or momentof force applied by the respective attachment device on the dentalappliance.

In one aspect, the one or more attachment devices may include aplurality of dental attachment devices provided on the tooth in anabutting position relative to each other, where the dental appliancemaybe configured to physically contact each of the plurality of theabutting dental attachment devices sequentially, and separately for apredetermined period of time.

A computer implemented method in accordance with another embodimentincludes establishing an initial position of a tooth, determining atarget position of the tooth in a treatment plan, calculating a movementvector associated with the tooth movement from the initial position tothe target position, determining a plurality of components correspondingto the movement vector, and modifying a cavity geometry of a dentalappliance for the tooth based on the plurality of components.

The movement vector may be determined based on FEA modeling. Themovement vector may also be based on physical force modeling.

Further, one or more of the plurality of components may include one ormore force vectors associated with the movement of the tooth from theinitial position to the target position, where the one or more forcevectors may be designed into the cavity geometry of the dental applianceto apply the corresponding one or more force associated with therespective one or more force vectors on the tooth.

The method may also include updating the cavity geometry of thepolymeric shell for the tooth to apply the determined plurality ofcomponents corresponding to the movement vector on the tooth toreposition to the tooth from the initial position to the targetposition.

In addition, the method may also include determining the level of forceassociated with the movement vector, where determining the level offorce may include determining one or more positions on the tooth surfaceto apply the movement vector, and configuring the cavity geometry of thepolymeric shell for the tooth to apply the movement vector at thedetermined one or more positions on the tooth surface.

A method of manufacturing a dental appliance in accordance with stillanother embodiment includes determining a treatment plan of a patient'sorthodontic condition, for each stage of the treatment plan, defining aninitial position of a tooth, determining a target position of the tooth,calculating a movement vector associated with the movement of tooth fromthe initial position to the target position, determining a plurality ofcomponents corresponding to the movement vector, and modifying a cavitygeometry of a polymeric shell for the tooth based on the plurality ofcomponents.

The method in one aspect may include generating a virtual representationof the modified cavity geometry.

A computer implemented method in accordance with still anotherembodiment may include establishing an initial position of a tooth,determining a target position of the tooth in a treatment plan,determining a sweep geometric path between the initial position and thetarget position and an associated movement vector for repositioning thetooth from the initial position to the target position, and modifying acavity geometry of a polymeric shell for the tooth based on thedetermined sweep geometric path, where modifying the cavity geometry mayinclude defining one or more contact points on an inner surface of thepolymeric shell for the tooth to contact a corresponding predeterminedone or more surfaces of the tooth.

Moreover, in still another aspect, modifying the cavity geometry mayinclude defining one or more protrusions on an inner surface of thepolymeric shell for the tooth, wherein the one or more protrusions isassociated with the movement vector.

The one or more protrusions may include a dimple.

Moreover, the cavity geometry may be modified to minimize frictionbetween an inner surface of the polymeric shell and the tooth.

A computer implemented method in accordance with still yet anotherembodiment may include establishing an initial position of a tooth,determining a target position of the tooth in a treatment plan,calculating a movement vector associated with the tooth movement fromthe initial position to the target position, determining a plurality ofcomponents corresponding to the movement vector, and determining one ormore positions for the placement of a corresponding one or more dentalattachment devices based on a respective surface area determination ofeach of the determined plurality of components corresponding to themovement vector.

In one aspect, the inner surface of a polymeric shell associated withthe treatment plan may be configured to apply a respective one or moreforces corresponding to the respective one of the plurality ofcomponents.

The method in one aspect may include determining a surface areasubstantially perpendicular to the direction of the movement vectorassociated with the tooth movement from the initial position to thetarget position.

The data processing aspects of the invention can be implemented indigital electronic circuitry, or in computer hardware, firmware,software, or in combinations of them. Data processing apparatus of theinvention can be implemented in a computer program product tangiblyembodied in a machine-readable storage device for execution by aprogrammable processor; and data processing method steps of theinvention can be performed by a programmable processor executing aprogram of instructions to perform functions of the invention byoperating on input data and generating output. The data processingaspects of the invention can be implemented advantageously in one ormore computer programs that are executable on a programmable systemincluding at least one programmable processor coupled to receive dataand instructions from and to transmit data and instructions to a datastorage system, at least one input device, and at least one outputdevice. Each computer program can be implemented in a high-levelprocedural or object oriented programming language, or in assembly ormachine language, if desired; and, in any case, the language can be acompiled or interpreted language. Suitable processors include, by way ofexample, both general and special purpose microprocessors. Generally, aprocessor will receive instructions and data from a read-only memoryand/or a random access memory. Storage devices suitable for tangiblyembodying computer program instructions and data include all forms ofnonvolatile memory, including by way of example semiconductor memorydevices, such as EPROM, EEPROM, and flash memory devices; magnetic diskssuch as internal hard disks and removable disks; magneto-optical disks;and CD-ROM disks. Any of the foregoing can be supplemented by, orincorporated in, ASICs (application-specific integrated circuits).

To provide for interaction with a user, the invention can be implementedusing a computer system having a display device such as a monitor or LCD(liquid crystal display) screen for displaying information to the userand input devices by which the user can provide input to the computersystem such as a keyboard, a two-dimensional pointing device such as amouse or a trackball, or a three-dimensional pointing device such as adata glove or a gyroscopic mouse. The computer system can be programmedto provide a graphical user interface through which computer programsinteract with users. The computer system can be programmed to provide avirtual reality, three-dimensional display interface.

Various other modifications and alterations in the structure and methodof operation of this invention will be apparent to those skilled in theart without departing from the scope and spirit of the invention.Although the invention has been described in connection with specificpreferred embodiments, it should be understood that the invention asclaimed should not be unduly limited to such specific embodiments. It isintended that the following claims define the scope of the presentinvention and that structures and methods within the scope of theseclaims and their equivalents be covered thereby.

1. A method of moving a tooth from an initial position to a targetposition, comprising: establishing the initial position of the tooth;determining the target position of the tooth in a treatment plan;determining a sweep geometric path between the initial position and thetarget position and an associated movement vector for moving the toothfrom the initial position to the target position; and modifying a cavitygeometry of a dental appliance for the tooth based on the determinedsweep geometric path.
 2. The method of claim 1, wherein modifying thecavity geometry includes defining one or more contact points on an innersurface of the dental appliance to contact a corresponding predeterminedone or more surfaces of the tooth.
 3. The method of claim 1, whereinmodifying the cavity geometry includes defining one or more features onan inner surface of the dental appliance, wherein the one or morefeatures is associated with the movement vector.
 4. The method of claim1, wherein the one or more features includes a dimple.
 5. The method ofclaim 1, wherein the cavity geometry is modified to minimize frictionbetween an inner surface of the dental appliance and the tooth.
 6. Themethod of claim 1, wherein the sweep geometric path is a union geometrybetween the initial position and the target position, wherein the uniongeometry comprises a plurality of increments of a position to asubsequent position in the treatment plan.
 7. The method of claim 1,wherein determining the sweep geometric path comprises determining apath that removes an interference between the initial position and thetarget position.
 8. The method of claim 1, wherein the movement vectoris configured to establish a force system applied by the dentalappliance to the tooth to move the tooth from the initial position tothe target position.
 9. The method of claim 8, wherein the force systemcomprises at least one of a force, a moment of a force, and a moment ofa couple.
 10. The method of claim 1, further including determining aplurality of components corresponding to the movement vector.
 11. Themethod of claim 10, wherein an inner surface of the dental appliance isconfigured to apply a respective one or more forces corresponding to therespective one of the plurality of components.
 12. The apparatus ofclaim 10, wherein the plurality of components may provide one or more ofa rotational displacement of the tooth, an angular displacement of thetooth, a linear displacement of the tooth, or one or more combinationsthereof.
 13. The method of claim 1, further comprising determining acorresponding position of one or more attachment devices relative to asurface plane of the tooth such that the one or more attachment devicesis configured to engage with the dental appliance at a contact point togenerate at least one of the components corresponding to the movementvector.
 14. The method of claim 1, further comprising determining asurface area substantially perpendicular to the direction of themovement vector associated with the tooth movement from the initialposition to the target position.
 15. The method of claim 1, furthercomprising fabricating the dental appliance using rapid prototyping. 16.The method of claim 1, wherein the dental appliance comprises apolymeric shell.
 17. A method of moving a tooth with a dental appliancehaving a specific cavity geometry, comprising: establishing an initialposition of the tooth; determining a target position of the tooth in atreatment plan; calculating a first movement vector associated withmovement of the tooth from the initial position to the target position;determining a component corresponding to the first movement vector; anddetermining a corresponding position of one or more attachment devicesrelative to a surface plane of the tooth such that the one or moreattachment devices is configured to engage with the dental appliance ata contact point to generate the component corresponding to the firstmovement vector.
 18. The method of claim 17, further comprisinggenerating a plurality of dental appliances having geometries selectedto progressively reposition the teeth, wherein the dental appliancescomprise polymeric shells having cavities and wherein the cavities ofsuccessive shells have different geometries shaped to receive andresiliently reposition teeth from one arrangement to a successivearrangement.
 19. The method of claim 17, wherein the plurality ofcomponents comprises at least one of a magnitude of a force and adirection of a force.
 20. The method of claim 17, wherein the attachmentdevice is configured to apply a predetermined force on the dentalappliance substantially at the surface plane of the tooth.
 21. Themethod of claim 17, wherein the plurality of components is configured toprovide one or more of a rotational displacement of the tooth, anangular displacement of the tooth, a linear displacement of the tooth,or one or more combinations thereof.
 22. The method of claim 17, whereinthe one or more attachment devices includes a plurality of dentalattachment devices provided on the tooth in an abutting positionrelative to each other.
 23. The method of claim 22, wherein the dentalappliance is configured to physically contact each of the plurality ofabutting dental attachment devices sequentially and separately for aperiod of time.
 24. The method of claim 17, further comprising attachingthe one or more attachment devices on the surface plane of the tooth.25. The method of claim 17, further comprising: after determining thecorresponding position of the one or more attachment devices,determining a second movement vector associated with movement of thetooth to a subsequent target position.
 26. The method of claim 25,further comprising modifying a shape of the dental appliance such thatthe dental appliance is configured to generate one or more componentscorresponding to the second movement vector.
 27. The method of claim 17,wherein the dental appliance comprises a polymeric shell.
 28. The methodof claim 17, further comprising fabricating the dental appliance usingrapid prototyping.
 29. An apparatus for modeling a dental appliance andpositioning of attachment devices for moving a tooth, comprising: a datastorage unit; a processing unit coupled to the data storage unit,wherein the processing unit is configured to determine a first positionof a tooth, determine a second position for the tooth in a treatmentplan, calculate a movement vector associated with a sweep geometric pathto move the tooth from the first position to the second position, 30.The apparatus of claim 29, wherein the data storage unit comprises adatabase comprising at least one patient treatment history; orthodontictherapies, orthodontic information, and diagnostics.
 31. The apparatusof claim 29 further including: determining a component corresponding tothe movement vector, and determining a position of one or moreattachment devices relative to a surface plane of the tooth such thatthe one or more attachment devices engages with the dental appliance ata contact point to generate the component corresponding to the movementvector.
 32. The apparatus of claim 31, wherein the one or moreattachment devices is configured to apply a predetermined force on thedental appliance substantially at the surface plane of the tooth. 33.The apparatus of claim 31, wherein the one or more attachment devicesmay include a plurality of dental attachment devices provided on thetooth in an abutting position relative to each other, wherein the dentalappliance may be configured to physically contact each of the pluralityof abutting dental attachment devices sequentially and separately for apredetermined period of time.
 34. The apparatus of claim 31, wherein theplurality of components may provide one or more of a rotationaldisplacement of the tooth, an angular displacement of the tooth, alinear displacement of the tooth, or one or more combinations thereof.35. The apparatus of claim 29, wherein the processing unit is furtherconfigured to modify a cavity geometry of the dental appliance based onthe sweep geometric path between the first position and the secondposition.
 36. The apparatus of claim 29, wherein the processing unit isfurther configured to define a contact point on an inner surface of thedental appliance to contact a corresponding predetermined surface of thetooth.
 37. The apparatus of claim 29, wherein the processing unit isfurther configured to define a feature on an inner surface of the dentalappliance, wherein the feature is associated with the movement vector.38. The apparatus of claim 29, wherein the sweep geometric path is aunion geometry between the first position and the second position,wherein the union geometry comprises a plurality of increments of aposition to a subsequent position in the treatment plan.
 39. Theapparatus of claim 29, wherein the movement vector is configured toestablish a force system applied by the dental appliance to the tooth tomove the tooth from the first position to the second position.
 40. Theapparatus of claim 39, wherein the force system comprises at least oneof a force, a moment of a force, and a moment of a couple.